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Theorem u3lem5 763
 Description: Lemma for unified implication study. (Contributed by NM, 24-Dec-1997.)
Assertion
Ref Expression
u3lem5 (a3 (a3 b)) = (ab)

Proof of Theorem u3lem5
StepHypRef Expression
1 comi31 508 . . 3 a C (a3 b)
21u3lemc4 703 . 2 (a3 (a3 b)) = (a ∪ (a3 b))
3 ax-a2 31 . . 3 (a ∪ (a3 b)) = ((a3 b) ∪ a )
4 u3lemona 627 . . 3 ((a3 b) ∪ a ) = (ab)
53, 4ax-r2 36 . 2 (a ∪ (a3 b)) = (ab)
62, 5ax-r2 36 1 (a3 (a3 b)) = (ab)
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   →3 wi3 14 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439 This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by:  u3lem6  767  u3lem14mp  794
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